Playing with Spaghetti: Vector and Raster Data Models in Depth

1
Playing with SpaghettiVector and Raster Data
Models in Depth

• Talbot J. Brooks
• ASU Dept. of Geography

2
Tonights topics

• Why we were gone
• Big picture overview Raster vs. Vector
• The details Vector data models
• The details Raster data models

3
Review you tell me

• What is the difference between vector and raster
  data?
• Basic vector data types
• Examples of raster data
• Computer file structures
• Flat
• Hierarchical
• Network
• Relational

4
RASTER AND VECTOR FORMATS
RASTER Grid-based, Simplify reality VECTOR
Analog map, Cartography
5
DATA MODEL OF RASTER AND VECTOR
REAL WORLD
1 2 3 4 5 6
7 8 9 10
1 2 3 4 5 6 7 8 9 10
GRID RASTER
VECTOR
6
RASTER DATA MODEL

• derive from formulation that real world - it has
  spatial elements and objects fills those elements
• real world is represented with uniform cells
• list of cells is a rectangle
• cell comprises of triangles, hexagon and higher
  complexities
• a cell reports its own true characteristics
• per units cell does not represent an object
• an object is represented by a group of cells

7
Lake
River
Pond
Reality - Hydrography
Lake
River
Pond
Reality overlaid with a grid
1
1
0
0
0
0
0
0
0
0
0
0
1
1
1
1
1
0
0
0
0
0
0
0
0 No Water Feature 1 Water Body 2 River
1
1
1
2
0
0
0
0
0
0
0
0
2
2
1
1
0
0
0
0
0
0
0
0
2
2
0
0
0
0
0
0
0
0
0
0
2
0
0
0
0
0
0
0
0
0
0
0
Resulting raster
Creating a Raster
8
VECTOR DATA MODEL

• derived from the formulation of spatial concepts
  that emphasize on real world objects
• geometry primitives of vector data model are
  point, line and polygon
• objects can be built from these primitives
• object location determined by represented
  location point
• uniqueness of vector data model lies in its
  management and storage of data geometry
  primitives
• spaghetti model
• topology model

9
VECTOR CHARACTERISTICS
POINT X LINE POLYGON
10
RASTER TO VECTOR
RIVER CHANGED FROM RASTER TO VECTOR FORMAT
RIVER THAT HAS BEEN
VECTORISED ORIGINAL RIVER
11
PRO AND CONS OF RASTER MODEL

• pro
• raster data is more affordable
• simple data structure
• very efficient overlay operation
• cons
• topology relationship difficult to implement
• raster data requires large storage
• not all world phenomena related directly with
  raster representation
• raster data mainly is obtained from satellite
  images and scanning

12
PRO AND CONS OF VECTOR MODEL

• pro
• more efficient data storage
• topological encoding more efferent
• suitable for most usage and compatible with data
• good graphic presentation
• cons
• overlay operation not efficient
• complex data structure

13
A look behind the scenes Vector GIS data models

• Spaghetti model
• Topological vector model
• Cardinality (this is gonna hurt!)
• Break

14
The Spaghetti Model

• The spaghetti model is the most simple vector
  data model
• The model is a direct representation of a
  graphical image
• NO explicit topological information

15
Spaghetti Model

• Description direct line for line translation of
  the paper map (often viewed as raw digital data)
• Pros easy to implement, good for fast drawing
• Cons storage and searches are sequential,
  storage of attribute data

16
Spaghetti model
17
Topology

• Branch of mathematics dealing with geometric
  properties
• Geometry of objects remain invariant under
  transformations
• Neighborhood relationships remain the same
• Topology is the distinguishing basis for more
  complicated vector models

18
Topological Vector Model

• Topological data models are provided with
  information that can help us in obtaining
  solutions to common operations in advanced GIS
  analytical techniques.
• This is done by explicitly recording adjacency
  information into the data structure, eliminating
  the need to determine it for multiple operations.
• Each line segment, the basic logical entity in
  topological data structures, begins and ends when
  it either contacts or intersects another line, or
  when there is a change in direction of the line.

19
Topological Vector Model

• Each line has two sets of numbers, a pair of
  coordinates and an associated node number.
• Each line segment has its identification number
  that is used as a pointer to indicate which set
  of nodes represent its beginning and ending.

20
Topological Vector Model

• Polygons also have identification codes that
  relate back to the link numbers. Each link in
  the polygon now is capable of looking left and
  right at the polygon numbers to see which two
  polygons are also stored explicitly, so that even
  this tedious step is eliminated.
• The Topological data model more closely
  approximates how we as map readers identify the
  spatial relationships contained in an analog map
  document.

21
Topological Vector Model
22
How do we preserve topology ina computer
database?

• What are we storing?
• Points, lines, polygons
• What do we need to preserve?
• Neighborhood relationships between these objects
• Terminology
• point, link, node, polygon

23
Terminology

• Point x, y coordinate identifying a geographic
  location
• Link (line, arc) an ordered set of points with a
  node at the beginning and end of it
• Node the beginning and end of link (often
  defined where 3 or more lines connect)
• Polygon two or more links connected at the
  nodes, contains a point inside to identify the
  polygons attributes

24
Nevada
Utah
California
Arizona
25
Identify the polygons
26
Create the polygon attribute table (PAT)
27
Identify the nodes
28
Node table
29
Identify the links (arcs, lines)
30
Simplify this
31
Create the topology!
32
Nodes First
33
Nodes First
34
Polygons
35
Polygons
36
Identify the points
37
Link List
38
Point Coordinates
39
Putting it all together
40
Putting it all together
41
Putting it all together
42
Putting it all together
43
Putting it all together
44
Cardinality

• Cardinality is the relationship between spatial
  objects, attributes, or spatial objects and
  attributes.
• This relationship may be defined as
• 11
• 1many
• manymany

45
Cardinality

• We can use cardinality to establish relationships
  and rules among objects and attributes
• This becomes the basis for modeling how data is
  arranged within a GIS - especially one that uses
  vector data.

46
Cardinality contd

• Entity-entity relationships are described by
  cardinality which may be
• One to one. A FOREST can have only one MANAGER
  and a MANAGER can have only one FOREST
• Many to one. Many FACILITIES may be contained
  within one FOREST
• Many to Many. The relationship water_supply may
  have many entries and may be connected to many
  entries FACILITIES, FOREST, etc

47
Cardinality contd

• The same concept applies to space
• A bathroom is located within a house (11)
• Many homes are within a town (many1)
• Many people are within many homes (manymany)

48
Diagram Characteristics

• Boxes represent entities
• Ovals represent attributes
• Diamonds represent relationships
• Note how cardinality is depicted
• Key attributes are underlined
• Multi-valued attributes are in double ovals

49
Entity-Relationship (ER) Diagrams A Conceptual
Model
50
Exercise work in pairs 10 minutes

• Create a simple ER diagram for your neighborhood
• Pick a feature that matches each geometry type
  (point, line). For example
• For points, you might pick fire hydrants and lamp
  posts
• For lines, you might pick streets and water mains
• For polygons, pick parcels or zip codes

51
Explanation of database types

• a database is a collection of non-redundant data
  which can be shared by different application
  systems
• implies separation of physical storage from use
  of the data by an application program, i.e.
  program/data independence
• changes can be made to data without affecting
  other components of the system.

52
Database types

• tabular ("flat file") - data in a single table
• hierarchical
• network
• relational

53
The ideal GIS database is one that maximizes the
uniqueness of every feature while minimizing
total data quantity
54
Hierarchical databases

• Developed in the 1960s by International Business
  Machines (IBM)
• Somewhat resembles real-world filing systems
• Tree-structured, similar to folder arrangements
  in a computer directory
• The database keeps track of the different record
  types, their attributes, and the hierarchical
  relationships between them
• The attribute which assigns records to levels in
  the database structure is called the key (e.g. is
  record a department, part or supplier?)

55
Features of a hierarchical model

• a set of record "types"
• e.g. supplier record type, department record
  type, part record type
• a set of links connecting all record types in one
  data structure diagram (tree)
• at most one link between two record types, hence
  links need not be named
• for every record, there is only one parent record
  at the next level up in the tree

56
Features (contd)

• e.g. every county has exactly one state, every
  part has exactly one department
• no connections between occurrences of the same
  record type
• cannot go between records at the same level
  unless they share the same parent
• diagram

57
Pros and cons

• data must possess a tree structure
• tree structure is natural for geographical data
• data access is easy via the key attribute, but
  difficult for other attributes
• in the business case, easy to find record given
  its type (department, part or supplier)
• in the geographical case, easy to find record
  given its geographical level (state, county,
  city, census tract), but difficult to find it
  given any other attribute

58
Pros and cons (contd)

• e.g. find the records with population 5,000 or
  less
• tree structure is inflexible
• cannot define new linkages between records once
  the tree is established
• e.g. in the geographical case, new relationships
  between objects
• cannot define linkages laterally or diagonally in
  the tree, only vertically

59
Pros and cons (contd)

• the only geographical relationships which can be
  coded easily are "is contained in" or "belongs
  to"
• DBMSs based on the hierarchical model (e.g.
  System 2000) have often been used to store
  spatial data, but have not been very successful
  as bases for GIS

60
Network data model

• developed in mid 1960s as part of work of CODASYL
  (Conference on Data Systems Languages) which
  proposed programming language COBOL (1966) and
  then network model (1971)
• other aspects of database systems also proposed
  at this time include database administrator, data
  security, audit trail
• objective of network model is to separate data
  structure from physical storage, eliminate
  unnecessary duplication of data with associated
  errors and costs

61
Networked model (contd)

• uses concept of a data definition language, data
  manipulation language
• uses concept of mn linkages or relationships
• an owner record can have many member records
• a member record can have several owners
• hierarchical model allows only 1n
• example of a network database
• a hospital database has three record types
• patient name, date of admission, etc.

62
Networked model (contd)

• doctor name, etc.
• ward number of beds, name of staff nurse, etc.
• need to link patients to doctor, also to ward
• doctor record can own many patient records
• patient record can be owned by both doctor and
  ward records
• network DBMSs include methods for building and
  redefining linkages, e.g. when patient is
  assigned to ward

63
Problems with the networked model

• links between records of the same type are not
  allowed
• while a record can be owned by several records of
  different types, it cannot be owned by more than
  one record of the same type (patient can have
  only one doctor, only one ward)

64
Relational database model

• the most popular DBMS model for GIS
• Used by ArcInfo
• flexible approach to linkages between records
  comes closest to modeling the complexity of
  spatial relationships between objects
• proposed by IBM researcher E.F. Codd in 1970
• more of a concept than a data structure
• internal architecture varies substantially from
  one RDBMS to another

65
Relational databases (contd)

• each record has a set of attributes
• the range of possible values (domain) is defined
  for each attribute
• records of each type form a table or relation
• each row is a record or tuple
• each column is an attribute
• note the potential confusion - a "relation" is a
  table of records, not a linkage between records
• the degree of a relation is the number of
  attributes in the table

66
Relational databases (contd)

• 1 attribute is a unary relation
• 2 attributes is a binary relation
• n attributes is an n-ary relation
• Examples
• unary COURSES(SUBJECT)
• binary PERSONS(NAME,ADDRESS) OWNER(PERSON
  NAME,HOUSE ADDRESS)
• ternary HOUSES(ADDRESS,PRICE,SIZE)

67
How a relational database works

• a key of a relation is a subset of attributes
  with the following properties
• unique identification
• The value of the key is unique for each tuple
• nonredundancy
• no attribute in the key can be discarded without
  destroying the key's uniqueness
• A prime attribute of a relation is an attribute
  which participates in at least one key
• All other attributes are non-prime

68
Relational database key example

• For example, a phone number is a unique key in a
  phone directory
• in the normal phone directory the key attributes
  are last name, first name, street address
• if street address is dropped from this key, the
  key is no longer unique (many Smith, Mary's)

69
Pros and cons

• the most flexible of the database models
• no obvious match of implementation to model -
  model is the user's view, not the way the data is
  organized internally
• is the basis of an area of formal mathematical
  theory

70
Pros and cons (contd)

• most RDBMS data manipulation languages require
  the user to know the contents of relations, but
  allow access from one relation to another through
  common attributes Example Given two relations
  PROPERTY(ADDRESS,VALUE,COUNTY_ID) COUNTY(COUNTY
  ID,NAME,TAX_RATE)
• to answer the query "what are the taxes on
  property x" the user would

71
Pros and cons (contd)

• retrieve the property record
• link the property and county records through the
  common attribute COUNTY_ID
• compute the taxes by multiplying VALUE from the
  property tuple with TAX_RATE from the linked
  county tuple

72
Data Interpolation

• Process of estimating the value of data at a
  location where no data were collected

73
Example

• Elevation data are collected at points
• Carbon Dioxide data were collected at points

74
Triangulated Irregular Network

• TIN is composed of
• nodes
• edges
• triangles
• hull polygons
• topology

75
Nodes

• The fundamental building blocks of the TIN
• They originate from the points and arc vertices
  contained in the input data sources.
• Every node is incorporated in the tin
  triangulation.
• Every node in the tin surface model must have a z
  value.

76
Creating Triangles
Delaunay criterion If you draw a circle around
the triangle with each of the points intersecting
the circle, no other point may fall within the
circle
77
Take the points, and draw triangles
78
Edges

• Every node is joined with its nearest neighbors
  by edges to form triangles which satisfy the
  Delaunay criterion.
• Each edge has two nodes, but a node may have two
  or more edges.

79
Triangles

• Each facet describes the behavior of a portion of
  the tins surface.
• The x,y,z coordinate values of a triangles three
  nodes can be used to derive information about the
  facet, such as slope, aspect, surface area, and
  surface length.

80
Hulls

• The hull is formed by one or more polygons
  containing the entire set of data points used to
  construct the tin.
• The hull polygons define the zone of
  interpolation of the tin.

81
Hull Types
Convex Hull
Hull
82
Topology

• Topology is maintained with information of each
  triangles nodes, edge numbers and type, and
  adjacency to other triangles.
• For each triangle, TIN records
• The triangle number
• The numbers of each adjacent triangle
• The three nodes defining the triangle
• The x,y coordinates of each node
• The surface z value of each node
• Also records the series of nodes that make up
  the hull

83
Example
84
Triangle topology
85
Coordinates and attributes
86
What can we do with TINs

• Calculate slope, aspect, and elevation at any
  point on the surface
• Because edges have a node with a z value at each
  end, it is possible to calculate a slope along
  the edge from one node to the other.

87
Calculating elevation along an edge
Using IDW (inverse distance weighting), we can
estimate the elevation value along any node
New Z (1000.5)(800.5) 90
88
In fact, we can estimate a z value anywhere in
our TIN
900.6 800.4 54 32 86
860.5 900.5 4345 88
89
Now, imagine doing this for each square dot
location
90
What youve created is a surface called a lattice

• Lattice rows and columns of continuous values

91
Comparison
Square Grid Tessellation
Lattice
92
Four sources

• Data that are collected in a raster format (e.g.,
  satellite data)
• Data in vector format converted to raster format
• Data in a paper map converted to raster format
• Interpolating data from points

Method of converting our TIN into a Lattice
93
In class exercise
94
Network Data Model
95
(No Transcript)
96
(No Transcript)
97
Some Terms

• Edges (links) Streets, transmission lines, pipe,
  and stream
• Junctions (nodes) Street intersections, fuses,
  switches, service taps, and the confluence of
  stream reaches are examples of junctions
• Impedance the cost associated with traveling
  along a specific link

98

• Edges connect together at junctions
• The flow from one edge to another edge through
  junctions
• Automobiles, electrons, water - can be
  transferred to another edge
• Impedance can be applied to edges or junctions

99
Types of networks

• Straight network (animal movement)
• Branching network (stream patterns)
• Circuit (street patterns)
• Directed flows can move in a single direction
• Undirected flows can move in either direction

100
Analysis of networks

• Connectivity
• gamma index ratio between the number of links in
  a network to the maximum possible
• alpha index ratio of the number of routes
  through a network to the maximum possible
• Shortest path

101
Gamma index
102
Gamma Index
103
(No Transcript)
104
(No Transcript)
105
Algorithm Terms

• Nodes
• Origin node
• Adjacent node
• Reached node
• Scanned node
• Unscanned node

• Cumulative Cost
• Tables
• Scanned table
• Reached table Cumulative Cost

106
(No Transcript)
107
(No Transcript)
108
Step One
109
Step Two
110
Step Three
111
Step Four
112
Step Five
113
Step Six
114
Step Seven
115
Step Eight
116
Step Nine
117
Step Ten
118
Step Eleven
119
Step Twelve
120
Step Thirteen
121
Break time!
122
Raster data
123
What type of data?

• Continuous data
• Examples elevation, temperature
• Square grid tessellation also called raster

124
Raster Models (tessellation)
125
Raster
Data values are stored in rows and columns
126
Two types

• Scanned Map images
• Digital Raster Graphic
• Other maps
• Tessellation Models
• Square Grid Tessellation
• Hexagon Tessellation

127
Scanned Maps

• Scanned map as a photograph
• The value of each cell represents the color on
  the map needs to be interpreted the way a
  paper/analog map is interpreted

128
Digital Raster Graphic (DRG)
There is typically another file linked with the
DRG, so that the geographic position of the
graphic is known
129
MapQuest
130
Maps or Images??
131
Summary of scanned maps

• Have the characteristics of an analog map in that
  the location information and the attributes are
  stored as a visual product
• No queries can be made based on the database

132
Tessellation Models

• Location-based spatial data model process of
  dividing an area into smaller, contiguous tiles
  with no gaps between them
• Types
• regular and irregular
• Uses continuous surfaces
• Pros easy to implement and manipulate
• Cons high data storage, output not cartographic
  quality

133
Spatial and Attribute Data

• Combined in a single file
• Unlike the scanned maps, they can be searched

134
Tessellation Models

• Regular

Most common
Rarely used
135
Tessellation models
Regular grid
136
Data

• Rows and columns containing the attribute value
  associated with each data layer
• The row/column location of the data value
  represents the spatial position
• Exact geographic position is typically
  established with header information before the
  rows and columns of data
• Also need knowledge of what the values represent
  (e.g., elevation in meters) typically part of
  the metadata

137
Rows and Columns
138
Geographic Position
origin
orientation
size of each cell
139
(No Transcript)
140
(No Transcript)
141
Sample data
142
Each cell has a value
143
Data File
Origin (x,y) Ymax (x,y) Row,col Cell size
144
Tessellation models
Hexagonal mesh
Primary advantage over square grid tessellation
is distance measurements. Important in
applications that need to spread distances evenly
- e.g., spread of forest fires
145
Distance between adjacent cells?
Example modeling the spread of a fire from one
cell to the next adjacent cell.
146
Distance measurements between cells is the same
in the hexagon model
147
Where do we get raster data? Four sources

• Data that are collected in a raster format (e.g.,
  satellite data)
• Data in vector format converted to raster format
• Data in a paper map converted to raster format
• DRG
• Converted into a tessellation database
• Interpolating data from points

148
One satellite data

• Example Landsat Thematic Mapper (TM) data from
  USGS

149
(No Transcript)
150
(No Transcript)
151
Multispectral

• Multispectral meaning that each cell has more
  than one value (different sections of the
  electromagnetic spectrum) associated with it
  (these are called bands)

152
Bands and Resolution

• Fixed spatial resolution (either 30 meters or 120
  meters) depending on the band

Landsats 4-5 Wavelength (micrometers) Resolution
(meters) Band 1 0.45-0.52 30 Band 2
0.52-0.60 30 Band 3 0.63-0.69 30 Band
4 0.76-0.90 30 Band 5 1.55-1.75 30
Band 6 10.40-12.50 120 Band 7 2.08-2.35
30
153
What can we do with the bands?

• Band 1 penetrates water for bathymetric mapping
  along coastal areas and is useful for
  soil-vegetation differentiation and for
  distinguishing forest types.
• Band 2 detects green reflectance from healthy
  vegetation, and
• Band 3 is designed for detecting chlorophyll
  absorption in vegetation.
• Band 4 data is ideal for detecting near-IR
  reflectance peaks in healthy green vegetation and
  for detecting water-land interfaces.
• The two mid-IR red bands on (bands 5 and 7) are
  useful for vegetation and soil moisture studies
  and for discriminating between rock and mineral
  types.
• The thermal-IR band on (band 6) is designed to
  assist in thermal mapping, and is used for soil
  moisture and vegetation studies.

154
False color

• Bands 4, 3, and 2 can be combined to make
  false-color composite images where band 4
  represents the red, band 3 represents the green,
  and band 2 represents the blue portions of the
  electromagnetic spectrum. This combination makes
  vegetation appear as shades of red, brighter reds
  indicating more vigorously growing vegetation.
  Soils with no or sparse vegetation range from
  white (sands) to greens or browns depending on
  moisture and organic matter content. Water bodies
  will appear blue. Deep, clear water appears dark
  blue to black in color, while sediment-laden or
  shallow waters appear lighter in color. Urban
  areas appear blue-gray in color. Clouds and snow
  appear bright white. Clouds and snow are usually
  distinguishable from each other by the shadows
  associated with clouds

155
False Color Example
156
False Color example
157
False Color example
158
With the same data (NDVI)
Normalized difference vegetation index
159
Where do we get raster data? Four sources

• Data that are collected in a raster format (e.g.,
  satellite data)
• Data in vector format converted to raster format
• Data in a paper map converted to raster format
• DRG
• Converted into a tessellation database
• Interpolating data from points

160
Second source for raster data

• Data that are in another format (either vector or
  paper map) and need to be converted to a raster
  format

161
Land use in vector format
To convert it, we need to decide what size each
cell needs to be. How do we decide? Minimum
mapping unit and spatial resolution.
162
Sort the database
163
Minimum mapping unit
164
Better
This would give us a 2 m cell size
165
Default settings
166
Resulting data
167
Resulting data
755 (default)
168
200 meters
169
100 meters
170
10 meters
171
(No Transcript)
172
(No Transcript)
173
(No Transcript)
174
Which is best?
vector
100 meter
10 meter
175
Area and database size comparisons
176
Three conversion from a paper map

• Scanning can convert to a DRG or into a square
  grid or hexagon database
• Same rules apply as with vector scanning best
  approach is to trace to mylar, then scan
• (my personal experience it is easier to vector
  digitize, then use software to convert to raster
  format)

Note with scanning you can create either a DRG
or a tessellation database
177
Database size can be a problem Compaction
Run length encoding
178
In some cases, there is very little you can do
179
Four sources

• Data that are collected in a raster format (e.g.,
  satellite data)
• Data in vector format converted to raster format
• Data in a paper map converted to raster format
• Interpolating data from points